Fuzzy stochastic finite element method for the hybrid uncertain temperature field prediction

For the hybrid uncertain temperature field prediction involving both random and fuzzy uncertainties in material properties, external loads and boundary conditions, this paper proposes a new numerical technique named fuzzy stochastic finite element method (FSFEM) by a combination of perturbation theory and moment method. Random variables are adopted to quantify the stochastic uncertainty with sufficient experiment data; whereas, fuzzy variables are used to represent the non-probabilistic parameters associated with expert opinions. By using the level-cut method, the fuzzy parameters are equivalently decomposed into interval variables. Based on the first-order Neumann series and random interval moment method, the interval bounds of the probabilistic characteristics of the uncertain temperature field are calculated effectively. Their membership functions are eventually reconstructed from the fuzzy decomposition theorem. By comparing the results with traditional Monte Carlo simulation, the numerical example demonstrates the feasibility and effectiveness of the proposed method for solving hybrid uncertain heat conduction problems in engineering.